Set 5: Quadratic Equations (Intermediate)

Explanation

Answer: A

The graph of $y = ax^2 + bx + c$ passes through the origin. What must be true?

$c = 0$

✓ Correct

$b = 0$

$a = 0$

$c = 1$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Passing through the origin means the point $(0, 0)$ is on the graph. 1. Substitute $x=0$ and $y=0$ into the equation. 2. $0= a(0)^2 + b(0) + c$ . 3. $0= 0 + 0 + c \Rightarrow c = 0$ . Choice B is incorrect because $b$ affects the vertex position. Choice C is incorrect because then it wouldn't be quadratic. Choice D is incorrect because then y-intercept would be 1.

Key Steps:

•

The correct answer is $c = 0$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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